Finite Group Databasebeta

← Group #286704

Character table — Group #286704

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444888888888888888844444444488888888888888882244888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-11-1
χ101111111111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-11
χ111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11
χ121111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11-1
χ131111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-111-1-111-1-1-11
χ141111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-111-1-1111-1
χ151111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1111-1
χ161111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-111-1-1-1-11111-1-11111-1-11111-1-1-11
χ17222222222-2222222-2-22-2-2-222-2-20000000022222222-200000000-2-200000000-2-200000000000000
χ18222222222-2222222-2-22-2-2-222-2-200000000-2-2-2-2-2-2-2-2-20000000022000000002200000000000000
χ19222222222-2-2-2-2-222-2-22-2-2-2-2-222000000002222-2-2-2-22000000002200000000-2-200000000000000
χ20222222222-2-2-2-2-222-2-22-2-2-2-2-22200000000-2-2-2-22222200000000-2-2000000002200000000000000
χ2122222222-222222-2-222-22-2-2-2-2220000000000000000-222-2-222-2-200000000000000000000000000
χ2222222222-222222-2-222-22-2-2-2-2220000000000000000-2-2-222-2-22200000000000000000000000000
χ2322222222-22-2-2-2-2-2-222-22-2-222-2-20000000000000000222-2-2-2-22200000000000000000000000000
χ2422222222-22-2-2-2-2-2-222-22-2-222-2-200000000000000002-2-22222-2-200000000000000000000000000
χ2522222222-2-22222-2-2-2-2-2-222-2-2-2-22i2i2i2i−2i−2i−2i−2i000000002000000000000002i2i−2i−2i0000000000000000
χ2622222222-2-22222-2-2-2-2-2-222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00000000200000000000000−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222222i2i2i2i−2i−2i−2i−2i00000000-200000000000000−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222−2i−2i−2i−2i2i2i2i2i00000000-2000000000000002i2i−2i−2i0000000000000000
χ2922-2-2-222-22-200002-22-2-222-2000022-2-222-2-200000000000000000002i2i−2i−2i0000000000002i−2i000000
χ3022-2-2-222-22-200002-22-2-222-2000022-2-222-2-20000000000000000000−2i−2i2i2i000000000000−2i2i000000
χ3122-2-2-222-22-200002-22-2-222-20000-2-222-2-22200000000000000000002i2i−2i−2i000000000000−2i2i000000
χ3222-2-2-222-22-200002-22-2-222-20000-2-222-2-2220000000000000000000−2i−2i2i2i0000000000002i−2i000000
χ3322-2-2-222-2-220000-22-222-22-200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000002i2i−2i−2i2-200000000
χ3422-2-2-222-2-220000-22-222-22-200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000−2i−2i2i2i-2200000000
χ3522-2-2-222-2-220000-22-222-22-20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000002i2i−2i−2i-2200000000
χ3622-2-2-222-2-220000-22-222-22-20000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000−2i−2i2i2i2-200000000
χ372-222-22-2-2022i2i−2i−2i00-2-20200002i−2i2−22−22−22−222−2−2i2i2−i2−i20002-2002i−2ii2−i20000i2−i2i2−i22−200000000000000
χ382-222-22-2-2022i2i−2i−2i00-2-20200002i−2i2−22−22−22−2−2−222−i2−i2i2i2000-2200−2i2i−i2i20000i2−i2i2−i2−2200000000000000
χ392-222-22-2-2022i2i−2i−2i00-2-20200002i−2i−22−22−22−2222−2−2i2i2−i2−i2000-2200−2i2ii2−i20000−i2i2−i2i22−200000000000000
χ402-222-22-2-2022i2i−2i−2i00-2-20200002i−2i−22−22−22−22−2−222−i2−i2i2i20002-2002i−2i−i2i20000−i2i2−i2i2−2200000000000000
χ412-222-22-2-202−2i−2i2i2i00-2-2020000−2i2i2−22−22−22−222−2−2−i2−i2i2i20002-200−2i2i−i2i20000−i2i2−i2i22−200000000000000
χ422-222-22-2-202−2i−2i2i2i00-2-2020000−2i2i2−22−22−22−2−2−222i2i2−i2−i2000-22002i−2ii2−i20000−i2i2−i2i2−2200000000000000
χ432-222-22-2-202−2i−2i2i2i00-2-2020000−2i2i−22−22−22−2222−2−2−i2−i2i2i2000-22002i−2i−i2i20000i2−i2i2−i22−200000000000000
χ442-222-22-2-202−2i−2i2i2i00-2-2020000−2i2i−22−22−22−22−2−222i2i2−i2−i20002-200−2i2ii2−i20000i2−i2i2−i2−2200000000000000
χ452-222-22-2-20-22i2i−2i−2i00220-20000−2i2ii2−i2i2−i2−i2i2−i2i222−2−2i2i2−i2−i202i−2i002-200−i2i20000−222−2−2200000000000000
χ462-222-22-2-20-22i2i−2i−2i00220-20000−2i2ii2−i2i2−i2−i2i2−i2i2−2−222−i2−i2i2i20−2i2i00-2200i2−i20000−222−22−200000000000000
χ472-222-22-2-20-22i2i−2i−2i00220-20000−2i2i−i2i2−i2i2i2−i2i2−i222−2−2i2i2−i2−i20−2i2i00-2200−i2i200002−2−22−2200000000000000
χ482-222-22-2-20-22i2i−2i−2i00220-20000−2i2i−i2i2−i2i2i2−i2i2−i2−2−222−i2−i2i2i202i−2i002-200i2−i200002−2−222−200000000000000
χ492-222-22-2-20-2−2i−2i2i2i00220-200002i−2ii2−i2i2−i2−i2i2−i2i222−2−2−i2−i2i2i202i−2i00-2200i2−i200002−2−22−2200000000000000
χ502-222-22-2-20-2−2i−2i2i2i00220-200002i−2ii2−i2i2−i2−i2i2−i2i2−2−222i2i2−i2−i20−2i2i002-200−i2i200002−2−222−200000000000000
χ512-222-22-2-20-2−2i−2i2i2i00220-200002i−2i−i2i2−i2i2i2−i2i2−i222−2−2−i2−i2i2i20−2i2i002-200i2−i20000−222−2−2200000000000000
χ522-222-22-2-20-2−2i−2i2i2i00220-200002i−2i−i2i2−i2i2i2−i2i2−i2−2−222i2i2−i2−i202i−2i00-2200−i2i20000−222−22−200000000000000
χ532-22-22-22-2202i−2i2i−2i-2-20020002i−2i00000000002i−2i2i−2i2-22-2000000000002−22−2000000i2−i2i2−i20000i2−i22−200
χ542-22-22-22-2202i−2i2i−2i-2-20020002i−2i00000000002i−2i2i−2i2-22-200000000000−22−22000000−i2i2−i2i20000−i2i2−2200
χ552-22-22-22-2202i−2i2i−2i-2-20020002i−2i0000000000−2i2i−2i2i-22-22000000000002−22−2000000i2−i2i2−i20000−i2i2−2200
χ562-22-22-22-2202i−2i2i−2i-2-20020002i−2i0000000000−2i2i−2i2i-22-2200000000000−22−22000000−i2i2−i2i20000i2−i22−200
χ572-22-22-22-220−2i2i−2i2i-2-2002000−2i2i00000000002i−2i2i−2i-22-22000000000002−22−2000000−i2i2−i2i20000i2−i2−2200
χ582-22-22-22-220−2i2i−2i2i-2-2002000−2i2i00000000002i−2i2i−2i-22-2200000000000−22−22000000i2−i2i2−i20000−i2i22−200
χ592-22-22-22-220−2i2i−2i2i-2-2002000−2i2i0000000000−2i2i−2i2i2-22-2000000000002−22−2000000−i2i2−i2i20000−i2i22−200
χ602-22-22-22-220−2i2i−2i2i-2-2002000−2i2i0000000000−2i2i−2i2i2-22-200000000000−22−22000000i2−i2i2−i20000i2−i2−2200
χ61444-4-4-4-44004-4-44000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ62444-4-4-4-44004-4-4400000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ63444-4-4-4-4400-444-4000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ64444-4-4-4-4400-444-400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ6544-4-4-444-44400004-4-44-4-4-440000000000000000000000000000000000000000000000000000000
χ6644-4-4-444-4-4-40000-444-444-440000000000000000000000000000000000000000000000000000000
χ674-44-44-44-4-404i−4i4i−4i4400-4000−4i4i00000000000000000000000000000000000000000000000000000
χ684-44-44-44-4-40−4i4i−4i4i4400-40004i−4i00000000000000000000000000000000000000000000000000000
χ694-4-44-4-444400000-4400-400000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ704-4-44-4-444400000-4400-40000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ714-4-44-4-444-4000004-40040000000000000000000000000000000000000000000022−22−22220000000000
χ724-4-44-4-444-4000004-400400000000000000000000000000000000000000000000−222222−220000000000
χ734-4-4-444-44040000004-40-40000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ744-4-4-444-44040000004-40-4000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ754-4-4-444-440-4000000-440400000022−22−222222−22−22220000000000000000000000000000000000000000000
χ764-4-4-444-440-4000000-4404000000−222222−22−222222−220000000000000000000000000000000000000000000
χ7788-888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).